The present application relates generally to an improved data processing apparatus and method and more specifically to mechanisms for forecast-based refinement and load balancing for prediction of advection-diffusion processes.
Convection is the collective motion of particles in a fluid and actually encompasses both diffusion and advection. Advection is the motion of particles along the bulk flow, while diffusion is the net movement of particles from high concentration to low concentration. Advection is typically described using the following partial differential equation:
                    ∂        ψ                    ∂        t              +          ∇              ·                  (                      u            ⁢                                                  ⁢            ψ                    )                      =  0Diffusion is typically described using the following partial differential equation:
            ∂      ψ              ∂      t        =      ∇          ·              (                  D          ⁢                                          ⁢                      ∇            ψ                          )            where ψ is the quantity in consideration, u is the fluid velocity, and D is the diffusion coefficient (sometimes called the diffusivity). While there are some nuances to the combined effect for convection (e.g. forced, natural, gravitational mechanisms), the general definition for convection is the total motion. That is, convection is the sum of fluid movement due to bulk transport of the media (like the water in a river flowing down a stream—advection) and the brownian/osmotic dispersion of a fluid constituent from high density to lower density regions (like a drop of ink slowly spreading out in a glass of water—diffusion). Thus, convection covers the sum of transport both by diffusion and by advection.
In meteorology and physical oceanography, advection often refers to the horizontal transport of some property of the atmosphere or ocean, such as heat, humidity or salinity, and convection generally refers to vertical transport (vertical advection). Advection is important for the formation of orographic clouds (terrain-forced convection) and the precipitation of water from clouds, as part of the hydrological cycle.